Technique for Designing Acoustic Microwave Filters Using Lcr-Based Resonator Models

1. A method of designing an acoustic microwave filter in accordance with frequency response requirements, comprising: generating a modeled filter circuit design having a plurality of circuit elements comprising an acoustic resonant element defined by an electrical circuit model that comprises a parallel static branch, a parallel motional branch, and one or both of a parallel Bragg Band branch that models an upper Bragg Band discontinuity and a parallel bulk mode function that models an acoustic bulk mode loss; optimizing the modeled filter circuit design to generate an optimized filter circuit design; comparing a frequency response of the optimized filter circuit design to the frequency response requirements; and constructing the acoustic microwave filter from the optimized filter circuit design based on the comparison.

2. The method of claim 1 , wherein the parallel static branch comprises a static capacitance, and the parallel motional branch comprises a motional inductance and a motional capacitance.

3. The method of claim 1 , wherein the electrical circuit model comprises at least one resistor that models an electrical loss of the acoustic resonant element.

4. The method of claim 1 , wherein the electrical circuit model comprises the upper Bragg Band discontinuity.

5. The method of claim 4 , wherein the Bragg Band branch comprises a series LRC circuit.

6. The method of claim 1 , wherein the electrical circuit model comprises the parallel bulk mode function.

7. The method of claim 6 , wherein the bulk mode function is a hyperbolic tangent function.

8. The method of claim 7 , wherein the hyperbolic tangent function is Y = h * ( 1 - 1 10 ( freq w ⁡ ( 10 6 - F b ) + 1 ) ) , where Y is the bulk mode loss in dB; h is a scaling factor used to match the loss of the bulk mode; F b is a frequency in Hz used to match the onset frequency of the bulk mode, w is a scaling factor used to match the steepness of the onset of the bulk mode, and freq is the frequency of the input signal.

9. The method of claim 1 , wherein the frequency response requirements comprises one or more of a frequency dependent return loss, insertion loss, rejection, and linearity.

10. The method of claim 1 , wherein the acoustic resonant element is one of a surface acoustic wave (SAW) resonator, a bulk acoustic wave (BAW) resonator, a film bulk acoustic resonator (FBAR), and a microelectromechanical system (MEMS) resonator.

11. The method of claim 1 , wherein the frequency response requirements comprises a pass band.

12. The method of claim 11 , wherein the passband is in the 500-3500 MHz range.

13. The method of claim 11 , wherein the passband is in the 300 MHz to 10.0 GHz range.

14. The method of claim 11 , wherein the passband is in the 300 MHz to 300 GHz range.

15. The method of claim 1 , wherein the modeled filter circuit design has an Nth order ladder topology.

16. The method of claim 1 , wherein generating the modeled filter circuit design comprises: defining a physical model of the acoustic resonant element; simulating the physical model of the acoustic resonant element to generate a first frequency response; simulating the electrical circuit model of the acoustic resonant element to generate a second frequency response; comparing the first and second frequency responses; and modifying at least one parameter in the electrical circuit model based on the comparison prior to the optimization of the modeled electrical filter circuit design.

17. The method of claim 16 , wherein the physical model of the acoustic resonant element is simulated using a Finite Element Model (FEM).

18. The method of claim 16 , wherein defining the physical model of the acoustic resonant element comprises selecting a parameter consisting of at least one of a material, one or more of a number of finger pairs, aperture size, mark-to-pitch ratio, and transducer metal thickness.

19. The method of claim 16 , wherein defining the physical model of the acoustic resonant element comprises: defining a first set of resonator characteristics for the acoustic resonant element; simulating the physical model of the acoustic resonant element to generate a second set of resonator characteristics; comparing the first and second sets of resonator characteristics; and modifying at least one parameter of the physical model of the acoustic resonant element based on the comparison.

20. The method of claim 19 , wherein each of the first and second sets of resonator characteristics comprises one or both of a resonant frequency and a static capacitance.

21. The method of claim 20 , wherein optimizing the modeled filter circuit design comprises optimizing the one or both of a resonant frequency and a static capacitance.

22. The method of claim 19 , wherein comparing the frequency response of the optimized filter circuit design to the frequency response requirements, comprises: simulating the electrical circuit model of the acoustic resonant element of the optimized filter circuit design to generate a third set of resonator characteristics; simulating the physical model of the acoustic resonant element to generate a fourth set of resonator characteristics; comparing the third set of resonator characteristics to the fourth set of resonator characteristics; modifying the parameter of the physical model of the acoustic resonator based on the comparison; simulating the physical model of the acoustic resonant element with the modified parameter to generate another frequency response; replacing the electrical circuit model of the acoustic resonant element in the optimized filter circuit design with the other frequency response to create a modified optimized filter circuit design; and simulating the modified optimized filter circuit design to create the frequency response.

23. The method of claim 22 , wherein each of the third and fourth sets of resonator characteristics comprises one or both of a resonant frequency and a static capacitance.